"Friar Tuck" was a criminal who dressed as the classic Christian monk from Robin Hood stories. This criminal accompanied fellow criminals posing as "Robin Hood" and "Little John." There is no reason to believe that "Friar Tuck" adopted this guise for any reason other than because it fit with the "Robin Hood" shtick this criminal crew was using. He was not a real monk any more than he was really an adherent of medieval Christianity.